Introduction to decision modelling

1. Introduction to decision modelling Andrew Sutton

2. Learning objectives Understand: • the role of modelling in economic evaluation • the construction and analysis of decision trees • the design and interpretation of a simple Markov model • the appropriate circumstances for their use

3. Role of modelling in economic evaluation • Extrapolate costs and effectiveness beyond trial data • Reflect all appropriate evidence • Compare all relevant options • Link intermediate clinical endpoints to final outcomes • Generalise results obtained in one clinical setting to other settings • Inform resource allocation decisions in the absence of “hard data” • Make head-to-head comparisons of alternative competing interventions when relevant trials do not exist

4. The main types of model • Decision trees • Markov models • Other types of models beyond this lecture

5. A decision model…. • has a structure to represent clinical pathways • allows synthesis of evidence to estimate costs and effectiveness • weighs up risks and benefits of an intervention • can allow events occurring over time • allows an assessment of different types of uncertainty • can identify priorities for future research

6. Decision Trees • Use for “one off” decisions • Particularly suited to • Acute care problems (“kill or cure”) • Once-only diseases • Short-term diagnostic/screening decisions

7. Steps in constructing and analysing decision trees • Structure the tree • Estimate probabilities • Estimate outcomes • Analyse the tree • Sensitivity analysis

8. Decision Tree Structure

9. Elements of a tree • Have one decision node at the root • The branches off the initial decision node represent all the strategies that are to be compared • A series of chance nodes off of each strategy branch • The outcomes at the end of each pathway

10. Decision Tree Example • Illustrative example: Heparin for the prevention of deep vein thrombosis (DVT) in hip replacement patients • Patients are at risk of DVT (and pulmonary embolism) post-surgery • Heparin can be injected pre-surgery and for 7-10 days post-surgery to try and prevent clots • However, there are risks of bleeding • The research question: • ‘Which is the more cost-effective treatment for hip replacement patients, heparin or conventional treatment?’

11. Decision tree for heparin

12. Estimating probabilities • Usually derived from published studies • Existing data: trial data or observational data • Meta analysis: aggregating from multiple sources • For each branch following a chance node, the conditional probability P is needed: • Probabilities are numbers between 0 and 1 • Probabilities for all branches out of a given chance node add to 1

13. Entering probabilities

14. Estimating outcomes • Outcomes include: • Total cost • Total utilities • Life years (LY) • Quality-adjusted life years (QALYs) • Outcomes are entered at terminal nodes

15. Costs and Utilities • Costs assumed for example here • Cost of heparin - £300 • Cost of conventional treatment - £50 • Cost of deep vein thrombosis event - £2000 • Cost of bleed - £500 • Utilities assumed • DVT – 0.70 • Bleed – 0.95 • DVT & bleed – 0.65 • No event – 1.00

16. Entering outcomes (QALYs) QALY Assume timeframe is one year

17. Entering outcomes (Costs) Cost £

18. Analysing the decision tree • Decision tree is averaged out and “rolled-back” to get the expected value for each strategy (work from terminal nodes towards decision nodes) • Expected value is the sum of products of the estimates of the probability of events and their outcomes

19. Example: analysing the tree (output as QALYs) A C B D F E

20. Rollback Calculations • Work from terminal nodes towards decision nodes • QALYs of heparin arm is Point A = (0.65*0.1) + (0.70*0.9) = 0.695 Point B = (0.95*0.1) + (1.0*0.9) = 0.995 Point C = (0.695*0.14) + (0.995*0.86) = 0.953

21. Rollback Calculations • QALYs of conventional treatment arm is Point D = (0.65*0.01) + (0.70*0.99) = 0.6995 Point E = (0.95*0.01) + (1.0*0.99) = 0.9995 Point F = (0.6995*0.25) + (0.9995*0.75) = 0.9245

22. Example: analysing the tree (output as costs)

23. Full structure of cost-effectiveness analysis

24. Example: Result from analysing the tree (CEA) ICER = 630 – 555 = 75 = £2500 per QALY 0.95 - 0.92 0.03

25. Sensitivity analysis • Previous calculations assume that probabilities and costs are known exactly • Suppose the cost of LMW heparin reduced to £200

26. Limitations of decision trees • Need to be able to assess full implications of each possibility (patient pathway) • Less suitable for longer-term outcomes • possible to add branches (not efficient) • Difficult to handle recurrence

27. Markov models • Markov models represent disease processes which evolve over time • Suited to modelling the progression of chronic disease • Can handle recurrence • Estimate long term costs and life years gained/QALYs

28. Simple Markov model WELL ILL DEAD

29. Elements of Markov models • Markov states should be mutually exclusive and exhaustive • Markov cycle length: a fixed period of time • Transition probabilities • Transition from one state to another at end of a single cycle • Fixed transition probabilities out of each state, adding up to 1 • Markov rewards • Values assigned to each health state that represent the cost and utility of spending one cycle in that state

30. Simple Markov model 0.97 0.9 WELL ILL 0.02 0.1 0.01 DEAD 1.0

31. Steps in constructing a Markov model • Define states and allowable transitions • Choose a cycle length • Specify a set of transition probabilities between states • Assign a cost and utility to each health state • Identify the initial distribution of the population • Methods of evaluation

32. Markov model: Simple example • Stroke prevention model • Atrial fibrillation is a chronic heart arrhythmia which increases the risk of stroke (ischaemic) • Therapy available to reduce the risk of stroke - e.g. warfarin • Disabling stroke incurs costs over a long period of time and reduces quality of life • A Markov model is designed to evaluate the cost-effectiveness of treatments to prevent stroke in AF • Following example will concentrate on model structure

33. Markov states • Patients are classified in one of three states • Well with atrial fibrillation (AF) (Health state 1) • Disabled from stroke (Health state 2) • Dead (Health state 3)

34. Stroke prevention: Markov states P11 P22 P12 WELL, AF STROKE P13 P33 P23 DEAD

35. Decide on a cycle length • Markov cycles - a constant increment of time • Choice of cycle length should • depend on the timing of events in disease process • depend on the study question and available data For stroke prevention example, time cycle could be one year

36. Define transition probabilities

37. Attach costs and utilities to states Each health state has a cost and utility attached

38. Define initial distribution of population • A set of starting probabilities is required to describe the initial distribution of the Markov cohort among the states • Determined by modellers • Start all patients in the same state (1 0 0) • Different proportion in different states (0.90 0.10 0)

39. Methods of evaluation • Cohort simulation • Hypothetical cohort of patients • Expected values • Deterministic • Monte Carlo simulation • Sample one patient at a time, specify number of patients (“trials”) • Random, stochastic • More in later modules

40. Stroke prevention: cohort analysis

41. Limitations of Markov models • No account taken of history • Assumes uniform population and equal and constant risk • May overcome these limitations by using a larger number of states • Alternatively use other methods (Individual sampling models, discrete event simulation)

42. Summary • Models provide a practical method to synthesise information from multiple sources • Decision trees suited to model one-off treatments and short-term effects • Markov models allow recurring processes to be modelled